Electromagnetic field

In physics, the electromagnetic field (also EM field) is the field that describes electromagnetic interaction. An electromagnetic field is a classical field produced by moving electric charges. Consisting of the combination of the electric field and the magnetic field, it is generated locally by any distribution of electric charge that varies over time and propagates in space in the form of electromagnetic waves.

In classical electrodynamics it is described as a tensor field; in quantum electrodynamics the interaction is seen as the exchange of zero-mass particles, photons.

The electromagnetic field interacts in space with electric charges and can occur even in the absence of them since it is a physical entity that can be defined independently of the sources that generated it. In the absence of sources, the electromagnetic field is called “electromagnetic radiation” or “electromagnetic wave”; being a wave phenomenon that does not require any material medium to spread in space and that travels at the speed of light in the vacuum.

The electromagnetic field interacts in space with electric charges and can occur even in the absence of them, being a physical entity that can be defined independently from the sources that generated it. In the absence of sources the electromagnetic field is called “electromagnetic radiation” or “electromagnetic wave”, being an undulatory phenomenon that does not require any material support to spread in space and that in vacuum travels at the speed of light. According to the standard model, the quantum of electromagnetic radiation is the photon, the mediator of electromagnetic interaction. The electric field E and the magnetic field B are usually described with vectors in a three-dimensional space: the electric field is a conservative force field generated in space by the presence of stationary electric charges, while the magnetic field is a non-conservative vector field generated by charges in motion.

The introduction of a field, in particular a force field, is a way to describe the mutual interaction between charges, that in vacuum happens at the speed of light. In the classic theory of electromagnetism this interaction is considered instantaneous, since the speed of light is approximately 300.000 kilometers per second, while in the relativistic treatment is taken into account that this speed is finite and the force between charges is manifested after some time: in this context it is correct to say that a charge interacts only with the field and this interacts only later on a possible second charge placed nearby. In this context the electromagnetic field is described by the theory of classical electrodynamics in covariant form, that is invariant under Lorentz transformation, and represented by the electromagnetic tensor, a tensor with two indices of which electric and magnetic field vectors are particular components. Finally, if we consider also the role of spin of charged particles, we enter in quantum electrodynamics field, where electromagnetic field is quantized.

Electromagnetic field and Maxwell’s equations

The discoveries of Oersted and Faraday demonstrated very clearly that electric field and magnetic field are two interdependent entities and that only under certain conditions – for example, in the absence of moving charges – they are distinct. In the years following the discoveries of these two scientists, the Scottish physicist James Clerk Maxwell (1831-1879) formulated his theory of the electromagnetic field, according to which even in vacuum variable electric fields produce magnetic fields and, vice versa, variable magnetic fields produce electric fields. The electromagnetic actions undergone by a body are therefore due to modifications in space of the physical properties of a region, the electromagnetic field, generated by electric charges and magnets.

Maxwell’s theory is synthesized by Maxwell’s equations, formulated by the Scottish physicist in 1873, which describe the behavior of the electromagnetic field and allow to predict the existence of waves that propagate and at the same time carry it, called electromagnetic waves, which also include light waves (which travel in vacuum at the speed of light, equal to about 300.000 km/s). The four equations of Maxwell connect the electric and magnetic fields and describe the mutual interactions.

The first two describe electric and magnetic fields and concern the existence of “charges” that produce them; in particular, the first one describes the electric field generated by stationary charges, according to Coulomb’s law; the second one establishes that there are no isolated magnetic charges, unlike what happens for electric charges, but that the north pole of a magnet is always linked to a south pole.

Maxwell’s third equation expresses the Faraday-Neumann law of electromagnetic induction, according to which a time-varying magnetic field produces an electric field.

The fourth Maxwell equation states that any current generates a magnetic field, both a direct current and a time-varying electric field: in the latter case we introduce a quantity called displacement current, which is not generated by moving electric charges, but produces magnetic effects comparable to a real current.

Maxwell’s equations for electrical and magnetic phenomena can be considered the equivalent of Newton’s equations for mechanics, because they allow to know, at least in principle, the situation in a past or future instant, knowing the initial conditions.

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